Reciprocating piston machines of this type are known (U.S. Pat. No. 6,705,841 B2), and are used in particular in motor vehicles as coolant compressors for cooling the interior of the vehicle. They include a housing, a drive shaft, and a swivel element situated in the housing which defines a variable swivel angle with respect to a plane perpendicular to the drive shaft, the swivel element being articulatedly connected to a driving element. The driving element is connected to the drive shaft in a rotationally fixed manner, so that a rotation of the drive shaft also results in a rotation of the driving element and of the swivel element connected thereto, about the axis of the drive shaft. Such a reciprocating piston machine is provided with at least one piston which is movably supported in a cylinder preferably extending parallel to the drive shaft and which cooperates with the swivel element in such a way that a rotation of the swivel element results in an axial lifting motion of the piston. The piston stroke is a function of the swivel angle, i.e., the angle defined by the swivel element and a plane extending perpendicular to the central axis of the drive shaft. This swivel angle is variable due to the fact that the swivel element is articulatedly connected to the driving element. The drive shaft is coupled, for example, to the engine of a motor vehicle; this means that the rotational speed of the reciprocating piston machine depends directly on the engine speed. A variation of the swivel angle of the swivel element, and thus of the piston stroke of the reciprocating piston machine, is used to allow adjustment of the delivery volume, i.e., the output, of the reciprocating piston machine, independently of the rotational speed. In particular it may be desirable to achieve a constant delivery output which is independent of the engine speed. On the other hand, it is also possible that at constant engine speed the delivery volume of the reciprocating piston machine is to be adjusted to a changed output requirement. To allow the swivel angle to be varied, the swivel element is connected, via two bearing pins oppositely situated on the same axis, to a guide sleeve which is supported so as to be axially displaceable on the drive shaft. A spring element acts on the guide sleeve with a force which pushes the swivel element into a starting position in which the swivel element is essentially perpendicular to the drive shaft. To allow a delivery output to be achievable at all when the reciprocating piston machine is started, a stop element is provided which causes the swivel element to assume a minimum angle with respect to the plane perpendicular to the central axis of the drive shaft when the engine of the motor vehicle is at a standstill, and upon startup a minimum piston stroke is present which is sufficient to build up the pressure necessary for further control of the swivel angle. In reciprocating piston machines of this type, the spring element is supported on a step of the drive shaft, for which purpose the drive shaft is designed so that its diameter is not constant over its axial extension. In such cases, the drive shaft is often provided with a larger diameter in the region of the driving element to allow absorption of the forces which occur in the transmission of the rotary motion of the drive shaft to the driving element and the swivel element. The diameter of the shaft may then be reduced in other regions of the axial extension of the drive shaft. Such a design of the drive shaft has the disadvantage that it is expensive and time-consuming to manufacture.